Capacitance requirement for isolated self-excited induction generator

Advanced knowledge of the minimum capacitor value required for self-excitation of an induction generator is of practical interest. To find this capacitor value two nonlinear equations have to be solved. Different numerical methods for solving these equations are known from previous literature. However, these solutions involve some guessing in a trial-and-error procedure. A new simple and direct method is developed to find the capacitance requirement under RL load. Exact values are derived for the minimum capacitance required for self-excitation and the output frequencies under no-load, inductive and resistive loads. These calculated values can be used to predict theoretically the minimum value of the terminal capacitance required for self-excitation. For stable operation C must be chosen to be slightly greater than C_min. Furthermore, it is found that there is a speed threshold, below which no excitation is possible no matter what the capacitor value. This threshold is called the cut-off speed. Expressions for this speed under no-load and inductive load are also given